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Title

Radicals and units in Ramanujan's work

Authors 1, 2, 3

Affiliations

  1. Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801, U.S.A.
  2. Department of Mathematics, National University of Singapore, Kent Ridge, Singapore 119260, Republic of Singapore
  3. Department of Mathematics, Southwest Missouri State University, Springfield, Missouri 65804, U.S.A.

Bibliography

  1. B. C. Berndt, Ramanujan's Notebooks, Part IV, Springer, New York, 1994.
  2. B. C. Berndt, Ramanujan's Notebooks, Part V, Springer, New York, 1998.
  3. B. C. Berndt, H. H. Chan and L.-C. Zhang, Ramanujan's class invariants and cubic continued fraction, Acta Arith. 73 (1995), 67-85.
  4. B. C. Berndt, H. H. Chan and L.-C. Zhang, Ramanujan's singular moduli, Ramanujan J. 1 (1997), 53-74.
  5. B. C. Berndt, H. H. Chan and L.-C. Zhang, Ramanujan's class invariants, Kronecker's limit formula, and modular equations, Trans. Amer. Math. Soc. 349 (1997), 2125-2173.
  6. B. C. Berndt, H. H. Chan and L.-C. Zhang, Ramanujan's association with radicals in India, Amer. Math. Monthly 104 (1997), 913-919.
  7. B. C. Berndt and R. A. Rankin, Ramanujan: Letters and Commentary, Amer. Math. Soc., Providence, 1995; London Math. Soc., London, 1995.
  8. H. H. Chan and S.-S. Huang, On the Ramanujan-Gordon-Göllnitz continued fraction, Ramanujan J. 1 (1997), 75-90.
  9. S.-Y. Kang, Ramanujan's formulas for the explicit evaluation of the Rogers-Ramanujan continued fraction and theta-functions, Acta Arith., to appear.
  10. T. J. Osler, Cardan polynomials and the reduction of radicals, preprint.
  11. S. Ramanujan, Question 525, solution by N. S. Aiyar, J. Indian Math. Soc. 6 (1914), 191-192.
  12. S. Ramanujan, Question 682, solution by 'Zero', J. Indian Math. Soc. 7 (1915), 160.
  13. S. Ramanujan, Question 1070, solutions by S. D. Chowla, N. B. Mitra, and S. V. Venkataraya Sastri, J. Indian Math. Soc. 11 (1919), 160.
  14. S. Ramanujan, Question 1076, J. Indian Math. Soc. 11 (1919), 199.
  15. S. Ramanujan, Notebooks (2 volumes), Tata Institute of Fundamental Research, Bombay, 1957.
  16. S. Ramanujan, Collected Papers, Chelsea, New York, 1962.
  17. S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa, New Delhi, 1988.
  18. G. N. Watson, Theorems stated by Ramanujan (XII): A singular modulus, J. London Math. Soc. 6 (1931), 65-70.
  19. H. Weber, Lehrbuch der Algebra, dritter Band, Chelsea, New York, 1961.
  20. L.-C. Zhang, Ramanujan's class invariants, Kronecker's limit formula and modular equations (II), in: Analytic Number Theory, Proc. Conf. in Honor of Heini Halberstam, Vol. 2, B. C. Berndt, H. G. Diamond, and A. J. Hildebrand (eds.), Birkhäuser, Boston, 1996, 817-838.
Acta Arithmetica
1998-1999/87/2
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Pages:
145-158
Main language of publication
English
Received
1998-01-27
Accepted
1998-06-15
Published
1998
Exact and natural sciences